000			02215nam a2200277Ia 4500
003			OSt
005			20240130194711.0
008			231229s9999 xx 000 0 und d
020			_a9781475756753
040			_cIISER BPR
041			_aEng
082			_a512.74 _bSER _223rd
100			_aSerre, Jean-Pierre
245		0	_aLocal fields
250			_a1st ed.
260			_aNew York: _bSpringer Science, _cc1979.
300			_aviii, 241p. : _b(pbk). ; _c22cm.
440			_aGraduate texts in mathematics ; _vVol. 67
520			_aThe goal of this book is to present local class field theory from the cohomo­ logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho­ mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray. Includes bibliography and index.
650			_aMathematics
650			_aField theory
650			_aHomology theory
942			_cBK _2ddc
947			_a4995.477455
948			_a0.22
999			_c3186 _d3186